M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation

Tao Zhang, Zhenhai Liu, Feipeng Qi, Yongjun Jiao, Tailin Wu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:75638-75666, 2025.

Abstract

Multiphysics simulation, which models the interactions between multiple physical processes, and multi-component simulation of complex structures are critical in fields like nuclear and aerospace engineering. Previous studies use numerical solvers or ML-based surrogate models for these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each for a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, existing numerical algorithms struggle with highly complex large-scale structures in multi-component simulations. Here we propose compositional Multiphysics and Multi-component PDE Simulation with Diffusion models (M2PDE) to overcome these challenges. During diffusion-based training, M2PDE learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, M2PDE generates coupled multiphysics and multi-component solutions by sampling from the joint probability distribution. We evaluate M2PDE on two multiphysics tasks-reaction-diffusion and nuclear thermal coupling–where it achieves more accurate predictions than surrogate models in challenging scenarios. We then apply it to a multi-component prismatic fuel element problem, demonstrating that M2PDE scales from single-component training to a 64-component structure and outperforms existing domain-decomposition and graph-based approaches. The code is available at github.com/AI4Science-WestlakeU/M2PDE.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhang25bb, title = {{M}2{PDE}: Compositional Generative Multiphysics and Multi-component {PDE} Simulation}, author = {Zhang, Tao and Liu, Zhenhai and Qi, Feipeng and Jiao, Yongjun and Wu, Tailin}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {75638--75666}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhang25bb/zhang25bb.pdf}, url = {https://proceedings.mlr.press/v267/zhang25bb.html}, abstract = {Multiphysics simulation, which models the interactions between multiple physical processes, and multi-component simulation of complex structures are critical in fields like nuclear and aerospace engineering. Previous studies use numerical solvers or ML-based surrogate models for these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each for a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, existing numerical algorithms struggle with highly complex large-scale structures in multi-component simulations. Here we propose compositional Multiphysics and Multi-component PDE Simulation with Diffusion models (M2PDE) to overcome these challenges. During diffusion-based training, M2PDE learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, M2PDE generates coupled multiphysics and multi-component solutions by sampling from the joint probability distribution. We evaluate M2PDE on two multiphysics tasks-reaction-diffusion and nuclear thermal coupling–where it achieves more accurate predictions than surrogate models in challenging scenarios. We then apply it to a multi-component prismatic fuel element problem, demonstrating that M2PDE scales from single-component training to a 64-component structure and outperforms existing domain-decomposition and graph-based approaches. The code is available at github.com/AI4Science-WestlakeU/M2PDE.} }
Endnote
%0 Conference Paper %T M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation %A Tao Zhang %A Zhenhai Liu %A Feipeng Qi %A Yongjun Jiao %A Tailin Wu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhang25bb %I PMLR %P 75638--75666 %U https://proceedings.mlr.press/v267/zhang25bb.html %V 267 %X Multiphysics simulation, which models the interactions between multiple physical processes, and multi-component simulation of complex structures are critical in fields like nuclear and aerospace engineering. Previous studies use numerical solvers or ML-based surrogate models for these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each for a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, existing numerical algorithms struggle with highly complex large-scale structures in multi-component simulations. Here we propose compositional Multiphysics and Multi-component PDE Simulation with Diffusion models (M2PDE) to overcome these challenges. During diffusion-based training, M2PDE learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, M2PDE generates coupled multiphysics and multi-component solutions by sampling from the joint probability distribution. We evaluate M2PDE on two multiphysics tasks-reaction-diffusion and nuclear thermal coupling–where it achieves more accurate predictions than surrogate models in challenging scenarios. We then apply it to a multi-component prismatic fuel element problem, demonstrating that M2PDE scales from single-component training to a 64-component structure and outperforms existing domain-decomposition and graph-based approaches. The code is available at github.com/AI4Science-WestlakeU/M2PDE.
APA
Zhang, T., Liu, Z., Qi, F., Jiao, Y. & Wu, T.. (2025). M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:75638-75666 Available from https://proceedings.mlr.press/v267/zhang25bb.html.

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